Keeping the excess temperature of heat generating mediums and circuitry devices below an allowable level is a great challenge. To facilitate the heat transfer process, it is significant to improve and optimize the geometric structure of the cooling tools. The present paper deals with the shape optimization of a tree-shaped inverted fin ('cavity') that is penetrated into a heat generating body and extracts the generated heat from the hot piece to a cold environment. The objective is to obtain the optimal geometry of the tree-shaped cavity that minimizes the peak (maximum) temperature of the medium subject to the volume (space) constraint. A numerical solution is performed to deliver the temperature field within the medium and the direct search method is used to reach the optimal situation. The optimization results indicate that the final (optimized) tree-shaped configuration performs the best over the existing single-root cavities introduced in the open literature. For example, the maximum excess temperature calculated in the final tree-shaped cavity with four branches was found about 50% lower compared to the best configuration investigated in the open literature. (C) 2017 Elsevier Ltd. All rights reserved.